TEL AVIV — Sirens sounded throughout southern Israel on Thursday, warning residents to take cover as at least 10 rockets, missiles and mortars were fired from the Gaza Strip and Israel launched an airstrike to destroy a rocket launcher.

The Israeli response was relatively muted, showing that at least for the moment, military officials were still weighing how to halt the projectiles from Gaza that left schools closed in several Israeli cities for a second day and sent residents scrambling for shelters.

Four mortars, four Kassam rockets and two longer-range Grad military-grade rockets were fired into Israeli towns, a police spokesman said. No one was injured. One longer-range Grad missile landed just north of the coastal city of Ashdod, which is less than 20 miles from Tel Aviv, in the deepest strike inside Israeli territory so far.

The unabated rocket and mortar fire — which followed a bombing in Jerusalem on Wednesday that killed a 59-year-old British woman and injured 38 — prompted calls inside Israel for a stiffer Israeli military response, while Egypt’s foreign minister, Nabil al-Arabi, urged Israel not to launch a new military offensive so as not to further inflame tensions in the Arab world, which is already roiling from revolutions.

The uptick in Palestinian attacks over the past week comes amid a stalemate in peace talks that have left negotiations on Palestinian statehood uncertain. Israel is technically in a state of war with the radical Islamist group Hamas, which rules the Gaza Strip, and so there is no diplomatic effort at the moment for trying to put an end to the attacks.

A blistering, deadly Israeli military offensive in 2009 against the Gaza Strip failed to stop the rocket and mortar fire, and Israeli military officials say Hamas’s military strength has only grown since.

At a news conference in Tel Aviv, visiting U.S. Defense Secretary Robert M. Gates and Israeli Defense Minister Ehud Barak were asked whether an aggressive Israeli response to the Jerusalem bus bombing and the rocket attacks from Gaza would play into the hands of extremists who want to scupper the prospect of Israeli-Palestinian peace talks.

Barak gave no indication that Israel would show restraint. “We will respond, we have to respond, and we are determined to bring back security to the region,” he said.

Gates echoed Barak in saying that Israel had the right to self-defense, but he was less forceful. “The Israelis will have to make their own decision on how to respond,” he said. “No sovereign state can tolerate having rockets fired at its people.”

Earlier, Gates said he wanted to urge Israeli and Palestinian officials to avoid using instability in the Arab world as an excuse to avoid peace talks. Besides meeting with Barak, Gates is scheduled Friday to see Israeli Prime Minister Binyamin Netanyahu and Salam Fayyad, the prime minister of the Palestinian Authority.

“I know there may be a temptation during this time of great uncertainty in the region to be more cautious about pursuing the peace process,” Gates said. “But in my meetings with Israeli and Palestinian leaders, I carry a different message: that there is a need and an opportunity for bold action to move toward a two-state solution.”

Craig Whitlock is an investigative reporter who joined The Washington Post as a staff writer in 1998. Among other things, he has specialized in reporting on national security and foreign affairs. He has reported from more than 60 countries.

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